Table Of ContentEURO Advanced Tutorials on Operational Research
Series Editors: M. Grazia Speranza · José Fernando Oliveira
Femke Kessels
Traffic Flow
Modelling
Introduction to Traffic Flow Theory
Through a Genealogy of Models
EURO Advanced Tutorials on Operational
Research
Serieseditors
M.GraziaSperanza,Brescia,Italy
JoséFernandoOliveira,Porto,Portugal
Moreinformationaboutthisseriesathttp://www.springer.com/series/13840
Femke Kessels
Traffic Flow Modelling
Introduction to Traffic Flow Theory Through
a Genealogy of Models
123
FemkeKessels
DepartmentofTransport&Planning
DelftUniversityofTechnology
Delft,TheNetherlands
Logistics,TourismandService
Management
GermanUniversityofTechnology
Muscat,SultanateofOman
Additionalmaterialtothisbookcanbedownloadedfromhttp://extras.springer.com.
ISSN2364-687X ISSN2364-6888 (electronic)
EUROAdvancedTutorialsonOperationalResearch
ISBN978-3-319-78694-0 ISBN978-3-319-78695-7 (eBook)
https://doi.org/10.1007/978-3-319-78695-7
LibraryofCongressControlNumber:2018938797
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To Emma,JuliaandSofie
Preface
This book shows the history of traffic flow modelling from the perspective of
modern day applications. Traffic flow models describe how vehicles travel over
roads, at which speeds, what the distance is between them, how long they take to
traveloveracertainroadsection,etc.Combiningthemodelswithotherinformation
supportsestimations aboutcurrentand futuretraffic states. This allowsanswering
questionsaboutthepresenceanddurationofcongestion,traveltimesandtraveltime
delays,emissionsand safetyassessment. In turn,the informationcan be used in a
varietyofapplicationsincludingtransportationplanningandtrafficcontrol.
Thisbookshowsthehistoricaldevelopmentoftrafficflowtheorybymeansofa
genealogicaltree of traffic flow models.The tree, includedon page 15, showsthe
maindevelopmentsintrafficflowmodelling.Thefocusonthehistoryoftrafficflow
modelsgivesthereaderinsightintothebasicsoftrafficflowmodellingallthrough
tothemostadvancedmodelsthatarecurrentlyunderdevelopment.Inaddition,the
bookdiscussesnumericalmethodswhichareappliedtocreatecomputersimulations
basedonthetrafficflowmodels.
Thehistoryoftrafficflowmodellingstartsinthe1930s.BruceD.Greenshields
presentedhisfindingsabouttherelationshipbetweenvehiclespeedandthedistance
between vehicles at the Annual Meeting of the Highway Research Board (United
States).Eventhoughhehadsomepredecessorsdoingsimilarresearch,Greenshields
isoftenconsideredthefounderofTrafficFlowTheory.The1940swerearelatively
quiet time for traffic flow theory, but from the mid 1950s many new models
were introduced. Most of these new models include dynamics of traffic flow, i.e.
they describe how traffic flows change over time, due to for examples changes in
inflowofvehiclesortrafficlightschangingcolour.Differenttypesofmodelswere
developedandappliedforroaddesign.However,researchinthisareamostlystalled
againinthe1980s.Fasterandeasiertousecomputersbroughta neweraoftraffic
flow research from the mid-1990s, resulting in most of the models that are still
applied today. Many of today’s applications require efficient numerical methods
for fast and accurate predictions. Applications include transportation planning,
road design, safety assessment, environmental assessment, traffic management,
evacuationplanningandrouteadvice.
vii
viii Preface
Previousversionsof this work were publishedas the state-of-the-artchapterin
the author’sPhD dissertation (2013)and as a review article in the EURO Journal
on Transportation and Logistics (2015). The book format gives more space to
providemorebasics,togomoreindepthintothemostimportantaspectsoftraffic
flow modellingandsimulation,andto includeproblemsets thatwill reinforcethe
newly gained knowledge and insights of the reader. Furthermore,the most recent
developmentsinthefieldoftrafficflowtheoryhavebeenincluded.
The book aims at students (MSc and PhD), researchers and practitioners who
want to learn more about the background of the models they are applying. No
preliminary knowledge about traffic is assumed. Some background in calculus
and differential equations is required, but references will be given for those who
need to refresh their knowledge. Problem sets are included at the end of each
chapter, with answers to selected problems in Chap. 8. Some of the exercises
requirethereadertoperformsimulations,forwhichsoftwareisprovidedonline,at
thepublisher’swebsite(http://extras.springer.com).Somepreviousexperiencewith
Octave(orMatlab)isusefulfortheseexercises.
After reading the book and exploring some of the problems, readers will
understandthemainconceptsintrafficflowmodellingandsimulationinsuchaway
thattheycan(1)chooseanappropriatemodelfortheirresearchorotherapplication
and build a simple but useful simulation tool based on this model;(2) understand
anewlypublishedscientificarticlethatbuildsontrafficflowtheory,modellingand
simulationpresentedinthisbook,reviewthatarticleandapplythemodels/methods
thatarepresented;(3)startdevelopingtheirownmodelsandnumericalmethodsto
createnewbranchesofthemodeltree.
Delft,TheNetherlands FemkeKessels
June2018
Acknowledgements
Theseedsofexpandingtheideaofthegenealogicalmodeltreeintosomethingtobe
used in educationwere plantedduringmy PhD research.When the editorsof this
series,GraziaSperanzaandJoséFernandoOliveira,invitedmetowriteaproposal,
IwasremindedoftheencouragementsfromSergeHoogendoornandRobertBertini
andI decidedto accept. After myproposalwas accepted,also Christian Rauscher
fromSpringerwasalwaysquicktorespondtoanyofmyquestions.Alsothanksto
the colleaguesin Delftwhogavevaluablefeedbackondraftversionsof(partsof)
thisbook,SergeHoogendoorn,HansvanLint,SimeonCalvertandMengWang.
When working on this book, I have been writing at many different places,
surrounded by even more different people. Many days I found inspiration and
motivationfromgoing to the shared office of our PersonalDevelopmentNetwork
and working in the same room as likeminded other ‘expat partners’. Thank you
Steven,Eveline,Tina,Chris,Hanna,EmmaandMaryamforjustbeingthereandthe
manycoffeesoutside!OnotherdaysIwenttotheGermanUniversityofTechnology
in Oman, to be around other academics: it was always worth the long drive and I
made good progress among my now colleagues to be. Thank you Heba, Amjaad,
Osman,Amaaniandallinternsforthehospitality!Still,allthistimespentoutside
thehousewasnotenoughandIoftenworkedathome,onlytobedisturbedincase
of‘bloodorfire’,whichfortunatelyneverhappened.IamforeverthankfultoRosa
whohasbeenagreathelpandcaretakerforourchildrenduringthesetimes.Thelast
bitofprogresswasmadenotinMuscat,butinDelft,amongcolleaguesandfriends
atDelftUniversityofTechnology.Alsothankyouforyourhospitality!
Finally,abigthankstomyfamily,mam,pap,Mia,Giel,ManonandNiels,who
havebeenencouragingmeandgivingmespacetogrowduringcalmandtumultuous
times. And of course thanks and hugs to those who helped me keep a balance
between all this serious stuff and love, fun, play and adventure:Emma, Julia and
Sofie.
ix
Contents
1 IntroductiontoTrafficFlowModelling ................................... 1
1.1 TrafficFlowModellingCycle.......................................... 2
1.2 ObservationsandPhenomena.......................................... 4
1.2.1 ObservingTraffic............................................... 4
1.2.2 PhenomenainTraffic........................................... 6
1.3 TrafficFlowModels .................................................... 8
1.3.1 Agent-BasedModelsandTheirVariables..................... 8
1.3.2 ContinuumModelsandEdie’sDefinitions.................... 9
1.3.3 ClassificationsofModels....................................... 11
1.3.4 TrafficFlow,FluidFlowandOtherComplexSystems ....... 12
1.4 ApproachandScopeofThisBook..................................... 13
1.4.1 TheGenealogicalModelTree.................................. 13
1.4.2 NumericalMethodsforComputerSimulation................ 14
1.4.3 OtherAspectsofTrafficFlowModelling ..................... 16
ProblemSet.................................................................... 17
FurtherReading ............................................................... 18
2 TheFundamentalDiagram................................................. 21
2.1 HighDensities,LowSpeedsandViceVersa .......................... 21
2.2 ShapesoftheFundamentalDiagram................................... 23
2.2.1 FundamentalDiagramsinMacroscopicModels.............. 23
2.2.2 FundamentalDiagramsinMicroscopicModels............... 25
2.3 PropertiesandRequirements........................................... 27
2.3.1 Requirements ................................................... 27
2.3.2 Properties:Capacity,FreeFlowandCongestion.............. 28
2.3.3 AdditionalRequirements....................................... 28
2.4 ScatterintheFundamentalDiagram................................... 29
ProblemSet.................................................................... 31
FurtherReading ............................................................... 34
xi
